# The graph of 3x-7y+11=0 crosses the y axis at which point?

Mar 15, 2018

The graph of color(red)(3x-7y+11=0 crosses the y axis at color(blue)((0, 1.571)

#### Explanation:

Find where the graph of color(red)(3x-7y+11=0 crosses the y axis.

The intercepts of a line are the points where the line intercepts, or crosses, the horizontal and vertical axes.

The straight line on the graph below intercepts the two coordinate axes. The point where the line crosses the x-axis is called the x-intercept.

The y-intercept is the point where the line crosses the y-axis.

Observe that the y-intercept occurs where $x = 0$, and the x-intercept occurs where $y = 0$.

Consider the given equation

$3 x - 7 y + 11 = 0$

Add color(brown)(7y to both sides of the equation, to get

$\Rightarrow 3 x - 7 y + 11 + \textcolor{b r o w n}{7 y} = 0 + \textcolor{b r o w n}{7 y}$

rArr 3x-cancel(7y)+11+color(brown)(cancel(7y)=0+color(brown)(7y)

$\Rightarrow 3 x + 11 = 7 y$

$\Rightarrow 7 y = 3 x + 11$

Substitute $x = 0$ to get

$7 y = 3 \left(0\right) + 11$

$7 y = 11$

$y = \frac{11}{7} \mathmr{and} y \approx 1.571428571$

Hence,

color(blue)(y=(0, 1.571) is the required y-intercept.

Hence, we can conclude that the graph of color(red)(3x-7y+11=0 crosses the y axis at color(blue)((0, 1.571)

Examine the image of the graph below for better comprehension: x-intercept occurs where $y = 0$.
If you substitute $y = 0$ in the given equation, you can get the x-intercept.